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-1.644666506.

(a) Plot the polynomial on the interval [-2, 1]. Hand in your plot with your

assignment.

(b) Use Newton's method with a tolerance of 10-¹0 to find the root. By trying

several different initial values, x₁, determine in what interval must you choose

₁ in order achieve convergence to x*. Explain why this is the case.

(c) Determine a function g(x) so that the fixed point iteration method is guaran-

teed to converge to r*. Explain why convergence is guaranteed for your choice

of g.

(d) Using the fixed_point (...) function provided, apply the fixed point method

with this g(x) and a tolerance of 10-10.

(e) Choose ₁ -2 and compare the speed of convergence (number of iterations

to achieve tolerance) of the two methods. Does this agree with the content of

the convergence theorems for the two methods?

Fig: 1